Simple answer to this. Go to the fly fishing department of any decent sized outdoor store, like Sportsman's, and buy a heavy duty retractor for holding trout nets. The one to get is the one with a threaded pin on it, not the clip-on version. You poke the sharp pin thru your Bino shoulder strap and fix it with the screw on plate, making it semi-permanent. Put it on your bow-holding hand side. You can put the rangefinder tether around your neck as insurance to not lose that $250 rangefinder!
When you are in an emerging shooting scenario, your draw hand goes up to the rangefinder on your shoulder, you range and drop the rangefinder. The retractable tether is strong enough to retract it out of the way as you go to full draw. With practice, you can range and shoot in 5-6 seconds. This system has worked flawlessly for me the last 7-8 years. If you're running and don't want it to flop around, simply unsnap it from the tether and put it in your pocket. You use the snap that comes with the tether for this.
This system goes for under $15.00. Hope someone tries it and likes it.